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curve or surface

資料來源 : Webster's Revised Unabridged Dictionary (1913)



   7. (Arith.) Three figures taken together in numeration; thus,
      140 is one degree, 222,140 two degrees.

   8. (Algebra) State as indicated by sum of exponents; more
      particularly, the degree of a term is indicated by the sum
      of the exponents of its literal factors; thus, a^{2}b^{3}c
      is a term of the sixth degree. The degree of a power, or
      radical, is denoted by its index, that of an equation by
      the greatest sum of the exponents of the unknown
      quantities in any term; thus, ax^{4} + bx^{2} = c, and
      mx^{2}y^{2} + nyx = p, are both equations of the fourth
      degree.

   9. (Trig.) A 360th part of the circumference of a circle,
      which part is taken as the principal unit of measure for
      arcs and angles. The degree is divided into 60 minutes and
      the minute into 60 seconds.

   10. A division, space, or interval, marked on a mathematical
       or other instrument, as on a thermometer.

   11. (Mus.) A line or space of the staff.

   Note: The short lines and their spaces are added degrees.

   {Accumulation of degrees}. (Eng. Univ.) See under
      {Accumulation}.

   {By degrees}, step by step; by little and little; by moderate
      advances. ``I'll leave it by degrees.'' --Shak.

   {Degree of a} {curve or surface} (Geom.), the number which
      expresses the degree of the equation of the curve or
      surface in rectilinear co["o]rdinates. A straight line
      will, in general, meet the curve or surface in a number of
      points equal to the degree of the curve or surface and no
      more.

   {Degree of latitude} (Geog.), on the earth, the distance on a
      meridian between two parallels of latitude whose latitudes
      differ from each other by one degree. This distance is not
      the same on different parts of a meridian, on account of
      the flattened figure of the earth, being 68.702 statute
      miles at the equator, and 69.396 at the poles.

   {Degree of longitude}, the distance on a parallel of latitude
      between two meridians that make an angle of one degree
      with each other at the poles -- a distance which varies as
      the cosine of the latitude, being at the equator 69.16
      statute miles.

   {To a degree}, to an extreme; exceedingly; as, mendacious to
      a degree.

            It has been said that Scotsmen . . . are . . . grave
            to a degree on occasions when races more favored by
            nature are gladsome to excess.        --Prof.
                                                  Wilson.

Center \Cen"ter\, n. [F. centre, fr. L. centrum, fr. round which
   a circle is described, fr. ? to prick, goad.]
   1. A point equally distant from the extremities of a line,
      figure, or body, or from all parts of the circumference of
      a circle; the middle point or place.

   2. The middle or central portion of anything.

   3. A principal or important point of concentration; the
      nucleus around which things are gathered or to which they
      tend; an object of attention, action, or force; as, a
      center of attaction.

   4. The earth. [Obs.] --Shak.

   5. Those members of a legislative assembly (as in France) who
      support the existing government. They sit in the middle of
      the legislative chamber, opposite the presiding officer,
      between the conservatives or monarchists, who sit on the
      right of the speaker, and the radicals or advanced
      republicans who occupy the seats on his left, See {Right},
      and {Left}.

   6. (Arch.) A temporary structure upon which the materials of
      a vault or arch are supported in position until the work
      becomes self-supporting.

   7. (Mech.)
      (a) One of the two conical steel pins, in a lathe, etc.,
          upon which the work is held, and about which it
          revolves.
      (b) A conical recess, or indentation, in the end of a
          shaft or other work, to receive the point of a center,
          on which the work can turn, as in a lathe.

   Note: In a lathe the

   {live center} is in the spindle of the head stock; the

   {dead center} is on the tail stock.

   {Planer centers} are stocks carrying centers, when the object
      to be planed must be turned on its axis.

   {Center of an army}, the body or troops occupying the place
      in the line between the wings.

   {Center of a} {curve or surface} (Geom.)
      (a) A point such that every line drawn through the point
          and terminated by the curve or surface is bisected at
          the point.
      (b) The fixed point of reference in polar co["o]rdinates.
          See {Co["o]rdinates}.

   {Center of curvature of a curve} (Geom.), the center of that
      circle which has at any given point of the curve closer
      contact with the curve than has any other circle whatever.
      See {Circle}.

   {Center of a fleet}, the division or column between the van
      and rear, or between the weather division and the lee.

   {Center of gravity} (Mech.), that point of a body about which
      all its parts can be balanced, or which being supported,
      the whole body will remain at rest, though acted upon by
      gravity.

   {Center of gyration} (Mech.), that point in a rotating body
      at which the whole mass might be concentrated
      (theoretically) without altering the resistance of the
      intertia of the body to angular acceleration or
      retardation.

   {Center of inertia} (Mech.), the center of gravity of a body
      or system of bodies.

   {Center of motion}, the point which remains at rest, while
      all the other parts of a body move round it.

   {Center of oscillation}, the point at which, if the whole
      matter of a suspended body were collected, the time of
      oscillation would be the same as it is in the actual form
      and state of the body.

   {Center of percussion}, that point in a body moving about a
      fixed axis at which it may strike an obstacle without
      communicating a shock to the axis.

   {Center of pressure} (Hydros.), that point in a surface
      pressed by a fluid, at which, if a force equal to the
      whole pressure and in the same line be applied in a
      contrary direction, it will balance or counteract the
      whole pressure of the fluid.
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